and the according triangular Bell-matrix Ut I could now compute some fractional iterates, which was not possible before.

There might be some mistake in my diagonalization-procedure due to fractional powers if the argument is complex. Because I could not locate the error yet I employed my new exponential polynomial interpolation. *In principle* this seems a start, the error seems to not to occur here.
(For the method see : http://go.helms-net.de/math/tetdocs/Expo...lation.pdf )

Anyway - things are still not yet fully satisfying. The range for parameters is very much limited, and there are still incompatibilities.
The ugliest problem is the divergence with complex numbers involved - the common summation-methods are simply not taylored for complex series. Sigh...